基于分数阶Fourier变换的模糊函数及其在二次调频信号参数估计应用中的研究

作为处理非平稳信号的一种重要工具，模糊函数(ambiguity function，AF)已经被广泛应用于雷达信号处理、声纳技术等领域，并对线性调频信号信号的参数估计具有极好的处理能力。但对应用于众多领域的二次调频信号，模糊函数就显得无能为力了。作为Fourier变换的更广义形式，分数阶Fourier变换(Fractional Fourier transform)近年来受到了广泛关注。为解决二次调频信号的估计问题，本文研究了基于分数阶Fourier变换的模糊函数，给出了这种变换的一些新的重要性质，如共轭对称性、Moyal公式、时移性等，推导出了它与经典模糊函数、基于分数阶Fourier变换的Wigner分布、短时Fourier变换、小波变换等其他时频变换的关系。作为应用,最后本文用这种分数阶模糊函数来估计二次调频信号，应用实例的仿真结果表明了分数阶模糊函数在估计二次调频信号参数方面的可行性和有效性。 

Research on the Ambiguity function based on the Fractional Fourier transform and its application for estimating the Quadratic FM signal

As an important tool for processing non-stationary signals,the ambiguity function(AF) has been widely used in radar signal processing,sonar technology,etc.It does well in estimating linear frequency modulation signals.However,it fails in estimating the Quadratic FM signal which is required in many fields.As the generalization of the Fourier transform,the fractional Fourier transform has attracted widespread attention these years.In this paper,in order to estimate parameters of Quadratic frequency modulation signals,we discuss the ambiguity function based on the fractional Fourier transform.Some new basic but important properties of the fractional ambiguity function are discussed,such as symmetry and conjugation property,shifting property and Moyal formula.As well the relationships between the fractional ambiguity function and other time-frequency analysis distributions are derived,including the classical ambiguity function(AF),the Wigner distribution function based on the fractional Fourier transform,the short-time Fourier transform(STFT),and the wavelet transform(WT).At last the fractional ambiguity function is applied for estimating the Quadratic frequency modulation signal.The simulation indicates that this new arithmetic is feasible and effective.